Speed of sound in a gas is v and r.m.s. veloc | vedclass

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(A) The speed of sound in an ideal gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $\

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$\sqrt{\frac{\gamma}{3}}$

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(A) The speed of sound in an ideal gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $\rho$ is the density.The $r.m.s.$ velocity of gas molecules is given by $c = \sqrt{\frac{3P}{\rho}}$.Taking the ratio of $v$ to $c$:$\frac{v}{c} = \frac{\sqrt{\frac{\gamma P}{\rho}}}{\sqrt{\frac{3P}{\rho}}} = \sqrt{\frac{\gamma P}{\rho} \cdot \frac{\rho}{3P}} = \sqrt{\frac{\gamma}{3}}$.Thus,the ratio is $\sqrt{\frac{\gamma}{3}}$.

Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is

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